About a year ago, as her home country was erupting in protests and plummeting ever more deeply into recession, Stephania Xydia graduated from London's City University and added a master's to her first class BA from Cambridge. She saw off stiff competition to be offered an internship at the Barbican, but decided instead on a course of action that raised eyebrows among those who knew her: she decided to come home to Greece.

Now, Xydia still has her old Raleigh bike, but instead of battling with London traffic she wends her way through the streets of Athens's historic Plaka neighbourhood, "under the Acropolis and the sun", to the cultural diplomacy NGO of which, aged 25, she is the managing director. "It's not easy," she concedes. "But I think it's worth investing a few years, working hard with no money, but trying to be part of change."

As their friends leave the country in droves, despairing at the lack of opportunity in a country where unemployment has reached 22% and more than 340,000 jobs were lost in the past year, some Greeks are swimming against the tide and choosing to stay put- or even, like Xydia, come home.

Occupying different positions on the political spectrum, with different backgrounds and different visions of the ideal future, they are united by one thing: a desire for their country to change and a belief in themselves to make it happen.

"There are two kinds of people who have stayed: those who are hopelessly pessimistic and those who are very optimistic," says Orestis Matsoukas, a 29-year-old entrepreneur who spent much of Greece's precariously-based boom years abroad but who, in a self-declared act of "perfect timing", returned to set up his business development consultancy just as the then prime minister George Papandreou went cap-in-hand to the IMF.

"The middle have left. The pessimists are saying: 'nothing's working.' We optimists feel that if we don't change things, who will? It's up to us."

Equipped with the skills picked up during their high-level educations and years spent abroad, both Matsoukas and Xydia feel their contribution to Greek society lies in their work. For her, that means helping a country steeped in remarkable history and culture to "liquidify its symbolic capital" and change its image abroad.

For him, it means encouraging young people to go into business and help ditch the old prevailing attitude among many Greek jobseekers that the public sector is best.

"Until less than two years ago, entrepreneurship was seen as something really negative," he says, relaxing over a beer after a long day in the Orama Group office. "When I was saying I wanted to be an entrepreneur, people were looking at me as though I was the devil."

Another thing Matzoukas and Xydia have in common is their intention in this Sunday's election: disgusted with the old guard, they could never vote for either the left-leaning Pasok or the centre-right Nea Demokratia (ND). Neither could they give their support, however, to Syriza, the leftwing coalition that is vying with ND for first place. For them it is a low-polling liberal party that is the best option – even if they know it doesn't stand a chance. "For me, whatever the result [of the election], it will be disastrous," says Xydia.

There are many, however, who could not disagree more. At 53, Dimitra Koutsis belongs to an older generation but has even more experience of life away from Greece, having lived in Canada from 1982 to 1998. Now, unemployed and surviving on the small pension of her late husband, she has one of two sons living in London and knows she could theoretically up sticks once more. But, she says, "the thought doesn't even cross my mind".

Standing outside a stall she is manning for Syriza, of which she is an active and hopeful member, the emotional implications of the issue are enough to make her voice catch.

Days later, in a suburban Athens cafe, she explains: "I'm determined to stay, to stay and fight in every sense. Because I think we shouldn't evacuate the country because it's going through a hard time. Although we've been humiliated by the media I'm still very proud of being Greek and I will always be proud."

Along with the non-payment of taxes and the wasteful spending, the purported failure of ordinary Greeks to do enough to help themselves through the crisis has become a feature of the kind of media coverage Koutsis despises.

For her part, she is channelling her energies into activism for Syriza, attending almost every demonstration, keeping herself informed, and making sure non-members are aware of what Alexei Tsipras's coalition stands for.

Tsipras is, she says, patriotic "in the right sense"- a reference, perhaps, to an ugly nationalism rearing its head in the form of the far-right Golden Dawn party. "It means loving your country from the ground to the people, the life you have here. It's like you have a child and you want the best for it, or a flower that you want to grow and blossom."

For others, too, there is potential for capitalising on a period in which the pieces of Greece's political kaleidoscope are still in flux.

Sotiris, a consultant who did not want his full name to be published, in an email to the Guardian said that he had tried to get involved with Syriza over the past two years "based on the 'romantic' idea that we can change things if we stop leaving the important decisions to a small group of politicians".

The 38-year-old said his family could easily move abroad. "But it would really hurt me to know that Greece is going to look like a third-world country for the next 20 to 30 years, meaning that my kids will not have the opportunity to choose if they want to live in Greece or not."

The chief reason for his staying, he said, was "to change Greece in the way I feel it has to change and give my children a better, fairer, more stable country in which to live."

Sometimes the aims are ambitious. Stavros Kalenterides, a 26-year-old who studied in Boston, volunteers with a public diplomacy NGO which, he says, "tries to go beyond traditional political lines" and will soon publish a proposal for a new Greek constitution.

But sometimes they are simple. Standing amid a bazaar in a leafy suburb of the capital, Iro, a member of a People's Assembly of activists formed from the protests of Syntagma Square, explains why the books and CDs on offer are for exchange and not for sale.

"This is about making alternative structures," she says. "It's actually a proposal for an alternative way of living." They want to change things, she explains, "by showing people there's another way of co-living".

And while times are hard, she would not be anywhere else. With that – if very little else – Matsoukas would agree. "At the moment, we don't really see a light at the end of the tunnel," he says. "There should always be a light. Even during the [Nazi] occupation there was a light. During the [colonels'] dictatorship there was a light. Now there's not. That's why I'm staying here. To find a light."